|
| |
|
|
A246815
|
|
Expansion of phi(-x) * psi(-x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
|
|
4
|
|
|
|
1, -2, -2, 4, 3, -2, -6, 4, 4, -6, -4, 4, 7, -8, -2, 8, 8, -4, -10, 4, 4, -10, -10, 8, 9, -4, -6, 12, 8, -6, -10, 12, 4, -14, -8, 4, 16, -10, -8, 8, 9, -10, -12, 12, 8, -12, -12, 4, 20, -10, -6, 20, 8, -6, -10, 12, 8, -20, -18, 8, 11, -12, -12, 16, 8, -6, -20
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
FORMULA
|
Expansion of q^(-1/2) * eta(q)^2 * eta(q^2) * eta(q^8)^2 / eta(q^4)^2 in powers of q
Euler transform of period 8 sequence [ -2, -3, -2, -1, -2, -3, -2, -3, ...].
a(n) = (-1)^floor((n+1) / 2) * A045828(n).
|
|
|
EXAMPLE
|
G.f. = 1 - 2*x - 2*x^2 + 4*x^3 + 3*x^4 - 2*x^5 - 6*x^6 + 4*x^7 + 4*x^8 + ...
G.f. = q - 2*q^3 - 2*q^5 + 4*q^7 + 3*q^9 - 2*q^11 - 6*q^13 + 4*q^15 + ...
|
|
|
MATHEMATICA
|
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x] EllipticTheta[ 2, Pi/4, x]^2 / (2 x^(1/2)), {x, 0, n}];
|
|
|
PROG
|
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^2 + A) * eta(x^8 + A)^2 / eta(x^4 + A)^2, n))};
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
